Most, if not all SOHO routers are switches with a Firewall, DHCP, and NAT added on them. The firewall aspect speaks for itself. It protects your LAN from intrusion. NAT allows multiple PC's to access the internet from a single IP address (the one provided by your ISP). DHCP, if you opt to use it allows you to automatically assign IP information to client computers on the network.
Switch is used to group computer within a network (the computers will on same network).
An enterprise level managed switch can allow multiple networks to reside on the same switch using VLAN's. So this isn't an absolute. In fact, with a 48 port switch, you could if you wanted, have 48 different VLAN's (subnets/networks) contained within a single switch.
Also, you can buy layer 3 switches that do routing as well....so a router isn't necessarily needed for routing.
For most small home environments you'll want a SOHO router between your DSL/cable modem and the LAN. This way you have a firewall protecting you from intrusion, which you won't get from just a regular switch.
If you have more PC's than you have LAN ports on the router, you purchase a small switch (unmanaged, unless you know a lot about managed switches and can afford one), plug it into a LAN port on the SOHO router and attach extra clients to the switch.
I can't seem to find any "gigabyte" type router, but switches seem more common.
You won't get 1000 Mbps access to the internet so if you really want it for your LAN, purchase an 8 port (or more if you have more than 8 PC's) gigabyte switch and plug all your clients into it and the switch in turn, into your SOHO router as I explained above. This will give all clients 1000 Mbps on the LAN. That is, providing of course all clients have 1000 Mbps NIC's in them.